On an inequality concerning the polar derivative of a polynomial

TL;DR

This paper provides a correct proof of an $L_p$-inequality related to the polar derivative of polynomials with restricted zeros and extends Zygmund's inequality to this context.

Contribution

It offers a rigorous proof of an $L_p$-inequality for polar derivatives and generalizes Zygmund's inequality to this setting.

Findings

Correct proof of the $L_p$-inequality for polar derivatives

Extension of Zygmund's inequality to polar derivatives

Enhanced understanding of polynomial inequalities with restricted zeros

Abstract

In this paper, we present a correct proof of an $L_p$-inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.